Find (a) E(X) (b) E (X²) (c) E [(X – 1)²]

Q: 2. The discrete random variable X has the probability function kx, x = 2,4, 6 P(X = x) = - 2), x = 8…

A: From the given information, it is clear that,  The discrete random variable X has a probability…

Q: f(x) dx = -4, f(x) dx = 6, g(x) dx = 8 - If g(x) dx b. c. 3f(x) dx d. dx x) - g(x)] dx g(x)] dx e.…

A:

Q: If f(x) is even and 5 [₁(f(x) - f(x) 8) dx = 8, find -5 5 [²³F(x) f(x) dx.

A: ∫-55fx-8dx=8 ∫-55fxdx-∫-558dx=8 ∫-55fxdx-8∫-55dx=8 As, ∫dx=x ∫-55fxdx-85--5=8 ∫-55fxdx-8×10=8…

Q: If E (X) = 1 and Var (X) = 4 then E (X² + 2X – 1) = :- 1)

A:

Q: Find an exponential function of the form f(x) = bax + c for the graph.

A: Given function-  f(x)= bax+c ----(A)  The curve (A)  is passing through ( -1,9) So putting x=-1 and…

Q: Let X - x? (s): (a) find E (X² +2x) where E (g (x)) = 6° g (x) fx (x) dx. %3D (b) find the…

A: Given

Q: d (7 ln(x)) dx Find

A: Find

Q: (3) E{g|(X)×g (Y)} = E[g{(X) × E{g2(Y)/X}] %3D

A:

Q: Find a formula for f(") (x) if f(x) = e-10: fln)(z) =[]

A:

Q: Show that E(X-µ)³ = E(x³) −3 [E (x²) ][E(X)] + 2[E(X)]³

A: The linearity of expectation property: With the assumption that, Xi's (i=1,2,...n) with n positive…

Q: Find a formula for f−1(x) and then verify that f−1(f(x))=x and ff−1(x)=x.   ​f(x)=

A:

Q: log(x – 2) V18 – 2x - 11. Find the domain of f(x) = (2, 9] O (2, 9] (2, 9) (2, 00) O (-00, 9)

A:

Q: Find the domain of v. v (x) = x + ln(7x - 4)

A: Find the domain of v. v (x) = x + ln(7x - 4)

Q: Let X be a random variable from the Pareto distribution with probability density function {(=10) = {…

A: Solution

Q: 22. Find expressions for f(g(x)) and g(f(x)), and state their domains a) f(x)=√√√x;g(x)=x²-4 f(g(x))…

A: Solution :- The domain of a function is the set of input or argument values for which the function…

Q: Find [2f(x) – g(x)]dx = i if f(x)dx = 4 and g(x)dx = 50

A:

Q: Expand the following expressions, TC(q) - 2TR(q) – FC (q) 5q – (3 – 2q)3 1 – ln (e2/9-x)2

A: we use some important formula given as below Part(a)  TC(q) -2TR(q) -FC(q)    Part(b) --

Q: Derive E(X|X>T)=E(X)+T

A: The condition is given that X is greater than T. Since, there is no other information about constant…

Q: (b) Find [x² -¹ J4(x) dx in terms of Jo(x) and J₁(x).

A: In the problem we have to find the value of the integration in terms of J0(x) and J1(x).  Here we…

Q: If f(x)dx=2a – 5b, then [f(x) – 2]dx=? a

A:

Q: Let g(x) = e5x Find g¹ (1) -1 Round your final answer to two decimal places.

A:

Q: | [10f(x) – g(x)]dx if Find 5 5 f(x)dx = 7 and g(x)dx = 6. %3D | [10f(x) – g(x)]dx = i

A:

Q: b. 8(x) = E ()" k = 1

A: domain: where function is defined

Q: Given f(x)=√x+1, g(x) = 3−*, h(x) = cosx, m(x) = log[-(x-4)] and p(x) = x-3 a. f(x) + g(x) b. g(x) -…

A:

Q: Calculate g(b)| and g' (b)|where g(x) is the inverse of f(x)= (x² + 6x)/²in the domain æ > 0f, where…

A:

Q: Find the function f(x) such that  f ′(x) = f(x)(1 − f(x)) and f(0) = 1/5.

A:

Q: ·S In (x) vxln(x)-x X dx

A: We know that integration power rule is - Integration of xn is xn+1/n+1 + C . Here C is integration…

Q: Find g(t) if g(t)= (f*g)(t) = L¹ ((-2/s +3/s² - 2/s³)F(s))

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Q: 9. Find f(35) (x) for f(x) = cos (2x)T = COS

A:

Q: Let X - x? (s). Find (a) E (1+2X + X²) where E (g (x)) = 6° g (x) fx (x) dx. (b) the characteristic…

A:

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: